Optimal allocation of units in sequential probability series systems

A concept of Sequential Probability Series System (SPSS) is developed in this paper, which widely exists in many practical sectors such as power plants, inventory management and security management. In SPSS the failure states of each unit are divided into two classes according to their consequences: dangerous failure and safe failure, where the former results in system failure while the latter has no impact on the system. Suppose that when a failure unit appears in SPSS, the system fails with probability p while the other units in SPSS can continue working with probability 1−p. This paper treats the problem of achieving optimal allocation of units in SPSSs that maximizes expected total working time of all units. Three optimal allocation models are formulated. We derive the analytical expressions for the optimal allocation solutions under certain assumptions. A genetic algorithm and a Monte Carlo method are provided to solve the allocation problems whose analytical solutions are difficult to obtain. An application can be found in Remote Power Feeding System (RPFS). Numerical examples for a RPFS are presented to demonstrate the application of the developed approach in each model.